If you had the problem with the IDE connector solder joints, I think you'd likely have more severe problems - failure to boot, and so forth. The fact that it plays and then bails sounds more like the cable, or a flakey disk. However, you have the new disk: it is likely that in replacing the disk you have damaged the connector on the cable, assuming you didn't remove the cable from the main board.

When the player starts to flake, pull it and feel the temperature. If it's really "ouch" hot, it's too hot. If you can hold your palm on it for a count of 10 without discomfort, it's not too hot.

I think you have a dodgy cable, and I would first try a careful re-crimp before anything else. I would normally make a pitch to sell you one, but - along with all my empeg spares, repair kit, and all the other bits I need - they are in a large box buried in a storage room about 10 km away. Sorry - speak to my (soon to be ex) wife about the inconvenience